Which of the following is equivalent to the logarithmic equation below? in x=3​

Answer:

$17,506.73

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\sf \implies A=10000e^{(0.07 \times 8)}[/tex]

[tex]\sf \implies A=10000e^{0.56}[/tex]

[tex]\implies \sf A=17506.725...[/tex]

Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.

Question:

A fair die is tossed.

Find the probability of obtaining an even number

Answer:

sample space=(1,2,3,4,5,6)

number of favourable outcomes=3

Event A= (outcome is even)

             = (2,4,6)

Total number of outcomes=6

Thus, P(even number)=3/6

                                      =1/2

Question 2:

A drawer contains 10 identical handkerchiefs of which 2 are white, 5 are blue, and 3 are pink. A handkerchief is drawn at random. what is the probability that it is white or pink?

Answer:

total number of outcomes=10

P(the handkerchief is white or pink)=2+3/10

                                                          =5/10

                                                          =1/2

Answer:

a

Step-by-step explanation:

The statement that is true about this function is C. As x approaches positive infinity, h(t) approaches positive infinity

Given that we have:

Therefore, when x approaches to negative infinity,

[tex]\lim_{x \to \infty} h(x)[/tex]

= 2^(-∞-5)

= 2^(-∞)

= 1/2^∞

=0

Also, as x approaches negative infinity, function h(x) approaches 0.

Then when x approaches to positive infinity,

[tex]\lim_{x \to \infty} h(x)[/tex]

2^(∞-5)

= 2^(∞)

= ∞

Therefore, As x approaches positive Infinity, h(x) approaches positive infinity.

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Answer:

100% probability or 1/1

Step-by-step explanation:

This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D

The volume of the square pyramid is the one-third of the square prism with same height and base area. Then the volume of the pyramid will be 120 cubic cm.

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

The volume of the square prism will be

V = (L × B × H)

Then the volume of the square pyramid is the one-third of the square prism with same height and base area.

[tex]\rm V_{pyramid} = \dfrac{V_{prism} }{3}[/tex]

A rectangular prism has a square base with a width of 6 and a volume of 360 cm³.

If a square pyramid has a base with the same width and height.

Then the volume of the pyramid will be

V = 360 / 3

V = 120 cubic cm

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[tex] \:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}[/tex]

[tex] \large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3[/tex]

Sum of two factors = 7 = 9 - 2

Product of these two factors = 9 × (-2) = 18

[tex]\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3[/tex]

[tex] \: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)[/tex]

[tex] \\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0[/tex]

Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.

[tex]\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2} \\ [/tex]

[tex] {6x}^{2} + 7x - 3 \\ \\ {6x}^{2} + 9x - 2x - 3 \\ \\ ( {6x}^{2} + 9x) - (2x + 3) \\ \\ 3x(2x + 3) - 1(2x + 3) \\ \\ (3x - 1)(2x + 3).[/tex]

It is clear that T lies on the perpendicular bisector of NP. See the explanation below.

Given that M (X,Y) is the midpoint of NP

X thus = (5+1)/2

= 3

Y = (7+1)/2

= 4

Hence, we have M (3,4)

Consequent on the above:

Slope TM (m') = (4-2) / (3-6) = - 2/3

Slope of NP (m) =  (7-1) / (5-1) = 6/4 = 3/2
M' = -1/m

Hence

TM ⊥ NP; and NP ⊥ TM

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Answer:

D. Intersecting lines.

Step-by-step explanation:

The lines are intersecting each other.

The reason it is not perpendicular lines is because perpendicular lines have 90° angles.

Hope this helps!

If not, I am sorry.

The function over the interval is an increasing exponential function.

A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".

The complete question is

An investment group compares returns on an account

against the function represented in the table, where x is the

time in years and f(x) is the total return on investment.

Which describes the function over the interval given in the

table?

х

a decreasing quadratic function

an increasing quadratic function

a decreasing exponential function

an increasing exponential function

0

5

f(x)

10,000

12,201.90

14,888.64

22,167.15

10

20

A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.

For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.

For, Exponential function          

When the exponential function then it shows total return on investment is not maximum.

When the exponential function is increasing it shows time goes, total return on investment is maximum.

Hence, the exponential function is increasing.

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Answer:

They are being multiplied by 2 each time.

Step-by-step explanation:

The X values are going up by 1 and every time X goes up by 1, Y doubles. So (1,2) goes to (2,4) and then (3,8) etc.

-11, -6, -7 and -6.1 are the answers

The inequality is r lesser than or equal to -6

Step-by-step explanation:

so, if I understand this correctly, the original square had a side length of 8 m.

now we transform this square into one with side length 1/4×8 = 8/4 = 2 m.

and the questions are what are the perimeter and the area of that new (smaller) square ?

the perimeter of a square is

4× side length = 4×2 = 8 m

the area of a square is

side length ² = 2² = 4 m²

Answer:

Exact Area of shaded region = 141.39cm²

Step-by-step explanation:

Quadrant of a circle - Quadrant refers to the four quarters in the coordinate plane system. Each of the four sections is called a quadrant. When it comes to circle, the quarter of a circle is called a quadrant, which is a sector of 90°.

area of circle  =πr²

area of quadrant of a circle = πr²/4

where r is the radius of the circle.

In the given figure there are 2 types of quadrants of circle are present

one with radius AB (bigger )

another with radius AB/2 (smaller)

Now area of quadrant having radius = AB

⇒ π(AB) ²/4

here AB is the side of square

so AB = 12cm

substituting this in the area of quadrant formula

area of bigger quadrant = π(12²)/4

                               area₁ = 144×π/4

                                area₁ = 144×3.142/4

                                area₁ = 113.112cm²

now area of smaller quadrant = π(AB/2) ²/4

                                    area ₂   = π(6) ²/4

                                    area ₂   = 36π/4

                                    area ₂   = 9×π

                                     area ₂  = 28.278cm²

Now it is clear from the given figure,

area of shaded region is =    area₁ -   area₂ +2×area₂

                                         =     113.112cm² -  28.278cm² + 2× 28.278cm²

                                         =     113.112cm² +  28.278cm²

                                         =      141.39cm²   (answer)

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Answer:

1/12

Step-by-step explanation:

dice rolling=1/6

coin flipping=1/2

Hence probability=1/6×1/2

Answer:

Dice roll = 1/6

Coin flip = 1/2

the transformations used are:

We start with the function:

[tex]f(x) = 2^x[/tex]

And we have the transformed function:

[tex]g(x) = 5*2^{x-2} + 3[/tex]

Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:

g(x) = 5*f(x).

Then we apply a shift of 2 units to the right, so we have:

g(x) = 5*f(x - 2)

Then we apply a shift of 3 units up, so we have:

g(x) = 5*f(x - 2) + 3

Replacing f(x) by the actual function:

[tex]g(x) = 5*2^{x-2} + 3[/tex]

Then the transformations used are:

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Answer:

5 dollars :)

Step-by-step explanation:

ig

The bearing from C to A of the given travel path is gotten as; 100.63°

From the bearing image attached, we can use trigonometric ratios to get;

tanx = opp/adj

x = 53 + θ ---------- eqn(1)

opp = 119

adj = 59

Thus;

tan x = 119/59

tan x = 2.0169

x = tan⁻¹(2.0169)

x = 63.63°

From eqn (1), we have;

θ = x - 53

θ = 63.63 - 53

θ = 10.63°

Thus, the bearing from C to A = 90 + 10.63 = 100.63°

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Answer:

where is  the question  Skidoo

this is just a statement

Answer:

20

Step-by-step explanation:

-10 + 20 = +10

Answer:

[tex]\fbox {20}[/tex]

Step-by-step explanation:

Let the required term be x

Then :

A triangle is a three-edged polygon with three vertices. ΔAKE and ΔCKP are congruent.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.

In ΔABC, since AB≅BC, therefore, the triangle will be an isosceles triangle, and the measure of ∠A ≅ ∠C, using the base angle theorem.

Now In ΔAKE and ΔCKP,

∠A ≅ ∠C {Proved above}

∠AKE ≅ ∠CKP {Given}

AK ≅ KC {Given }

Since two angles and a side of the triangle are equal, therefore, we can write the two triangle are congruent using the Side-angle-side or Angle-Side-Angle congruence.

Hence, ΔAKE and ΔCKP are congruent.

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Answer:

Step-by-step explanation:

Wrong

m∠R > m∠T

Correct

m∠S + m∠T < 90°

m∠S = m∠T

m∠R > m∠S

m∠S > m∠T

Answer:

Correct Answers:

m∠R > 90°

m∠S + m∠T < 90°

m∠R > m∠T

m∠R > m∠S

Wrong Answers:

m∠S = m∠T

m∠S > m∠T

Step-by-step explanation:

Finished on assignment. Found error is last response! Updated 7/2022

Answer: (C) r² = (x+5)²+(y-4)²

Solution:-

The given endpoints are (-7,1) and (-3,7)

so the center will be at the mid point of the line connecting these two points.

hence, center ={ (-7+-3)/2, (1+7)/2 }

hence, C= (-5,4)

so, the equation of the circle is:-

⇒ (x-(-5))²+(y-4)²=r²

or, (x+5)²+(y-4)²=r²

The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is

[tex]\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}[/tex]

Answer:

400

Step-by-step explanation:

4/5×500

=400 6s would be riled

Answer: b/5

Step-by-step explanation:

They divide the total by 5 to get the cost each person has to pay

Correct answer is option D.

The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).

For this case, the first thing you should observe is that you have a different function in two distinct intervals.

We have then:

For [-10, 2]:

The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)

For [2, 10]:

We have a constant function whose equation is:

y = 5

Thus, the correct Answer is:

D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.

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Answer:

the answer is (3,4) is the solution to line A but not to line b

Answer:

$99 000

Step-by-step explanation:

[tex](180000)(\frac{55}{100} )=99000[/tex]

Hope this helps